To mitigate the stains, you need to know what they are....
oil/grease/etc....good old fashion dish detergent like Dawn and an old fashioned scrub brush. You can get the kind on a stick, but it is easier to apply elbow grease down close. rinse with clean water from a hose. Some synthetic oils will be tougher and may need some methanol alcohol to remove, then the soap. The key is to soak up as much as you can (think kitty litter/oil dry) WHEN it happens, and to PREVENT it when ever possible. I have an old plastic tarp and a moving blanket that I use when working in the driveway. Plastic tarp, then the old blanket, then the work. oil dri stays nearby in a 5 gallon bucket.
nature stains are tougher...as you don't really know what they are. start with the weakest "solution" possible and work up from there. IE, soap and water, then some clorox/weak bleach mixed with water and let it soak a bit, not more than an hour or so, and rinse well.
Then you can step up to some of the more caustic "driveway cleaners", commercial cleaners, or abrasives and pressure.
But you have to be careful with each, they each have consequences and some may take more than one application with some nature time in between.
Now as to the pressure washer, especially if this is your first house..set it aside. There is nothing on a modern house that requires using a pressure washer to clean. I have family members who have the top of the line pressure washer, some one of each gas and electric. And they have all paid the price for improper use.
The pressure washer will easily knock the paint and gel coat from a truck cap, similarly it will rip the soft grain from a deck or anything made of real wood, they can render vinyl siding dull and remove the finish, paint from your mowing machine, even break windows, and peel auto trim from the body.
They are good for removing grafitti from cinderblock, decent for removing mud/concrete from construction equipment and if you are careful, the cat's meow, for cleaning boat bottoms when used promptly after the boat is hauled. But even then if you are not careful, you can blast a hole in 1/2" fiberglass.
Didn't say where you are, but concrete can take a long time, especially when poured in inclement weather or when additives are used to expedite things, to cure, and you may have a "quality" issue with your contractor, but the pics don't show the normal spalling associated with that. IMHO. Others may chime in.
All the best,